Robust foreign portfolio investment inflows and export proceeds continued to give the rupee strong underlying support, despite relatively firm greenback overseas.
Meanwhile, domestic bourses continued their impressive record-setting run for the second-straight session on hardening hopes of strong economic reforms even as the government gears up to unveil a national goods and services tax later this year.
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Forex dealers said weakness in the dollar against some other currencies overseas provided further momentum to the rupee.
The domestic currency resumed modestly lower at 65.07 as compared to Monday's close of 65.03 at the Interbank Foreign Exchange following sustained demand for the American currency from importers and banks.
It remained under immense pressure and drifted further to touch an intra-day low of 65.17 amid some caution ahead of the central bank policy meet.
However, overcoming the early volatility, the rupee staged a smart rebound in afternoon deals to hit a high of 64.85 before ending at 64.87, revealing a solid gain of 16 paise, or 0.25 per cent.
The rupee had lost 18 paise on Monday.
In worldwide trade, the greenback retreated against its major trading rivals after North Korea fired a ballistic missile into the sea ahead of a summit between US and Chinese leaders.
The dollar index, which tracks the US currency against a basket of six major rivals, was marginally up at 100.43.
The RBI, meanwhile, fixed the reference rate for the dollar at 65.0438 and for the euro at 69.4017.
In cross-currency trade, the rupee also rebounded against the pound sterling to finish at 80.97 from 81.30 per pound and continued to firm up against the euro to settle at 69.26 compared to 69.28 earlier.
But, the local unit remained weak against the Japanese Yen to conclude at 58.53 per 100 yens from 58.38.
On the equity front, the flagship Sensex jumped 64.02 points to finish at a new peak of 29,974.24 after revisiting the significant 30,000-mark briefly in early trade and the broader NSE-Nifty also rose 27.30 points to end at a lifetime high of 9,265.15.
In the forward market today, premium for dollar continued to rule firm owing to sustained paying pressure from corporates.
The benchmark six-month premium for September moved up to 155-157 paise from 153-155 paise and the far-forward March 2018 contract also edged up to 306.5-308.5 paise from 303.5- 305.5 paise on Monday.
On the global commodity front, crude oil prices hit an one-month high after data showed US crude inventories fell more than forecast.
The front-month WTI and Brent contract gained 1.57 per cent and 1.98 per cent, respectively.
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